Asymptotic stability and instability of the solutions of systems with impulse action

In this paper, we study the stability of the zero solution of a system of ordinary differential equations subject to impulse action. Using the method of Lyapunov functions, we obtain tests for asymptotic stability or instability of the system. Illustrative examples are given.     

基于不确定性回报的行为控制博弈分析

不确定型的行为控制较之确定型的行为控制更为复杂,但在现实中又有一定的广泛性,且目前的研究基础比较薄弱.把研究的视角放在不确定性回报下行为控制的博弈机理上,考察了博弈双方的行为观测偏差,定义了在信息不对称条件下管理者对被管理者的行为的观测矩阵、管理者的博弈策略矩阵、被管理者对管理者观测能力的估计矩阵及对管理者博弈策略的估计矩阵等,分析了管理者与被管理者之间的动态博弈过程和行为策略选择,给出了满足博弈均衡的不确定性回报的设计要求.这些都可以推广应用于各种具体管理制度的设计和改进当中,为行为控制研究提供了定量分析的新方法.在此基础上,选择房地产投资开发行为控制机制的实例进行了诊断研究.     

A construction of classifying spaces for p-adic group actions

One major open problem in geometric topology is the Hilbert-Smith conjecture. A natural approach to this conjecture is to work on classifying spaces of p-adic integers. However, the well-known Milnor's construction of classifying space of p-adic integers is not locally connected, hence will not help to solve the conjecture, and the other known constructions are very complex. The goal of this paper is to give a new construction of classifying spaces for p-adic group actions.     

Teichmüller curves,Galois actions and $ \widehat {GT} $‐relations

Teichmüller curves are geodesic discs in Teichmüller space that project to algebraic curves C in the moduli space M_g. Some Teichmüller curves can be considered as components of Hurwitz spaces. We show that the absolute Galois group G_? acts faithfully on the set of these embedded curves. We also compare the action of G_? on π₁(C) with the one on π₁(M_g) and obtain a relation in the Grothendieck–Teichmüller group, seemingly independent of the known ones. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Transverse Dimension of R~n Actions on Compact Foliated Manifolds

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Connections Between the Riemann and the Lorentz Force Laws

It is known that for the magnetic force due to a closed circuit, the Weber force law can be identical to the Lorentz force law. In this investigation it is shown that for both the electric and the magnetic force of the quasi-static case, the Riemann force law can be identical to the Lorentz force law, while the former is based on a potential energy depending on a relative speed and is in accord with Newton's law of action and reaction.     

3-幂零矩阵的Jordan标准型在GL_n(F)共轭作用下的迷向子群

研究迷向子群的结构是有限域上典型群几何中的一个重要问题.刻画了3-幂零矩阵的Jordan标准型在GLn(F)共轭作用下的迷向子群的结构.     

作用在n维欧氏空间R~n上的离散交叉积

主要研究作用在n维欧氏空间R~n上的离散交叉积■_n■_αG_A,b_1,…,b_n的代数性质与因子分类.首先证明了该交叉积是内射的;其次给出了该交叉积为因子的一些充要条件;最后讨论该交叉积为因子时究竟是几型因子.     

A note on the quantum Hamilton-Jacobi formalism

The postulates which have been introduced recently in order to obtain a quantum Hamilton-Jacobi formalism, starting from the classical one, are revised. It is shown that some of them can be replaced by alternative assumptions which happen to be much more natural. The quantum Hamilton-Jacobi equation is obtained as an eigenvalue equation on the quantum wave amplitude.